Setting parent to armature with automatic weights deforms the mesh
First of all try to align your bone. It can help a lot for a better rig. For doing that follow this step : show the axes of your bones, enter in the edit mode of your rig and align your bone with the roll property on the right pannel of the 3D view. You can see an exemple in the screen below!

Now you can do your automatic weight. 
I looked a bit on your rig and apparently you played a bit with it. You have to reset all the roation of your bone in pose mode.

Go in pose mode, select all bones with a and types alt+r.

And now you have to play a bit with the pole angle of your IK modifier for align all your bone. 

Normally with this 3 tips your armature has a better set up.